I've added some still from a gif which hopefully communicate what I'm trying to achieve. Basically, as the little red sphere is moved around in space the other spheres react and only show the side that is closest to the red sphere. There's also some cool animates on the vertices that happen as it goes.
Any advice on what to start looking into to learn more would be helpful, even knowing what this sort of phenomenon is called would be great.
Thanks!
------UPDATE-------
This is my current progress. I get the effect of masking half of the object but I suppose I more want to only render the faces that within view, not do a hard clip on them like in the gif above.